The cooling system has two functions. The first and most important is to keep the engine at a manageable temperature. the cooling is used to cool the engine as well as protect the engine and gaskets from rust, corrosion, and rot. the coolant temperature is maintained by a thermostat that keeps the coolant in the radiator long enough to cool it. The portion of coolant in the engine stays in the engine, cooling the engine till it's temperature is no longer manageable and then the thermostat releases it back into the radiator for cooling off. The second function is to provide heat to the vehicle's cabin (passenger compartment), the coolant passes through the heater control valve that transfers the coolant to a heater core, from here air is blown across the heater core's fins to produce warm air that is blown throw ducts and out to the cabin.
Cooling system operation and integrity are critical to a functioning engine, without it an engine cannot run for a longer time or last for long.